QU ICK START ( con t . )

How to change the template color theme You can easily change the color theme of your poster by going to the

DESIGN menu, click on COLORS, and choose the color theme of your choice.

You can also create your own color theme.

You can also manually change the color of your background by going to

VIEW > SLIDE MASTER. After you finish working on the master be sure to go

to VIEW > NORMAL to continue working on your poster.

How to add Text The template comes with a number of pre-

formatted placeholders for headers and text

blocks. You can add more blocks by copying and

pasting the existing ones or by adding a text box

from the HOME menu.

Text size Adjust the size of your text based on how much content you have to

present. The default template text offers a good starting point. Follow the

conference requirements.

How to add Tables To add a table from scratch go to the INSERT menu and

click on TABLE. A drop-down box will help you select rows and

columns.

You can also copy and a paste a table from Word or another PowerPoint

document. A pasted table may need to be re-formatted by RIGHT-CLICK >

FORMAT SHAPE, TEXT BOX, Margins.

Graphs / Charts You can simply copy and paste charts and graphs from Excel or Word. Some

reformatting may be required depending on how the original document has

been created.

How to change the column configuration RIGHT-CLICK on the poster background and select LAYOUT to see the

column options available for this template. The poster columns can also be

customized on the Master. VIEW > MASTER.

How to remove the info bars If you are working in PowerPoint for Windows and have finished your poster,

save as PDF and the bars will not be included. You can also delete them by

going to VIEW > MASTER. On the Mac adjust the Page-Setup to match the

Page-Setup in PowerPoint before you create a PDF. You can also delete

them from the Slide Master.

Save your work Save your template as a PowerPoint document. For printing, save as

PowerPoint of “Print-quality” PDF.

Print your poster When you are ready to have your poster printed go online to

PosterPresentations.com and click on the “Order Your Poster” button.

Choose the poster type the best suits your needs and submit your order. If

you submit a PowerPoint document you will be receiving a PDF proof for

your approval prior to printing. If your order is placed and paid for before

noon, Pacific, Monday through Friday, your order will ship out that same

day. Next day, Second day, Third day, and Free Ground services are offered.

Go to PosterPresentations.com for more information.

Student discounts are available on our Facebook page.

Go to PosterPresentations.com and click on the FB icon.

© 2013 PosterPresentations.com 2117 Fourth Street , Unit C Berkeley CA 94710

posterpresenter@gmail.com

(—THIS SIDEBAR DOES NOT PRINT—)

DES IGN GU IDE

This PowerPoint 2007 template produces a 36”x48”

presentation poster. You can use it to create your research

poster and save valuable time placing titles, subtitles, text, and

graphics.

We provide a series of online tutorials that will guide you

through the poster design process and answer your poster

production questions. To view our template tutorials, go online

to PosterPresentations.com and click on HELP DESK.

When you are ready to print your poster, go online to

PosterPresentations.com

Need assistance? Call us at 1.510.649.3001

QU ICK START

Zoom in and out As you work on your poster zoom in and out to the level that

is more comfortable to you.

Go to VIEW > ZOOM.

Title, Authors, and Affiliations Start designing your poster by adding the title, the names of the authors,

and the affiliated institutions. You can type or paste text into the provided

boxes. The template will automatically adjust the size of your text to fit

the title box. You can manually override this feature and change the size of

your text.

TIP: The font size of your title should be bigger than your name(s) and

institution name(s).

Adding Logos / Seals Most often, logos are added on each side of the title. You can insert a logo

by dragging and dropping it from your desktop, copy and paste or by going

to INSERT > PICTURES. Logos taken from web sites are likely to be low

quality when printed. Zoom it at 100% to see what the logo will look like

on the final poster and make any necessary adjustments.

TIP: See if your school’s logo is available on our free poster templates

page.

Photographs / Graphics You can add images by dragging and dropping from your desktop, copy and

paste, or by going to INSERT > PICTURES. Resize images proportionally by

holding down the SHIFT key and dragging one of the corner handles. For a

professional-looking poster, do not distort your images by enlarging them

disproportionally.

Image Quality Check Zoom in and look at your images at 100% magnification. If they look good

they will print well.

ORIGINAL DISTORTED

Corner handles

Go

od

pri

nti

ng

qu

alit

y

Bad

pri

nti

ng

qu

alit

y

performance: resolution, detection, …?

Compressive acquisition : sparse sensing [7]

- fewer measurements: processing gain and SNR critical!

- spatial–temporal measurements 𝒚 for joint angle-Doppler

𝒚 = 𝑨𝒙 + 𝒛, 𝑨𝑚𝑛 = 𝑒𝑗 μ𝑚u𝑛+𝑡𝑚v𝑛 , 𝒛~𝐶𝑁 𝟎, γ𝑰

sampling: spatial m and temporal t for angle u and Doppler v

Sparse-signal processing (SSP, e.g. [5] and [8]): a sparse model-based refinement of existing radar signal processing ([9]).

𝒙SSP = argmin𝒙

𝒚 − 𝑨𝒙 2+ η 𝒙 1

measured 𝑃res,SSP =P 𝑥SSP,𝑖 ≠ 0 ∧ 𝑥SSP,𝑗 ≠ 0 | 𝐻1

Information Geometry (IG) is stochastic signal processing where the stochastic inferences are structures in differential geometry ([2]-[3]).

The intrinsic geometrical structure of a data model is characterized locally by the Fisher information metric (e.g. [4], [6], [10], [11]):

𝐺uv

= −E𝜕2 ln 𝑝 𝒚 u, v

𝜕 u v 𝑇= 2SNR

𝑀t 𝛍 2 0

0 𝑀s 𝒕 2 = 𝑮0

Information distances between 𝑝 𝒚 u, v and 𝑝 𝒚 u + δu, v + δv :

𝑑𝛉 = 𝑑(𝛉, 𝛉 + δ𝛉) ≡ min𝛝 𝑡

𝛝 𝑡 𝑇𝐺 𝛝 𝑡 𝛝 𝑡 𝑑𝑡 1

0

𝑑(u

v,u + δuv + δv

) = 2 SNR 𝑀t 𝛍δu 2 + 𝑀s 𝒕δv 2 .

Resolution: testing 𝐻0: δ𝛉 = 𝟎 and 𝐻1: δ𝛉 ≠ 𝟎 [2]

GLR = 𝑝 𝒚 𝛉, 𝛉 + δ𝛉 𝑝 𝒚 𝛉 |δ𝛉=δ𝛉 ML

GLR test: asymptotic ln GLR~ χε,dim(𝛉)2 [12]

ε ≡ 𝑑𝛉2

Probability of resolution at separation δ𝛉 and SNR

𝑃res,GLRig = P ln aGLR > ρ | 𝐻1

ρ = χ0,dim(𝛉)2,inv (𝑃fa) and in SSP: η = −γln𝑃fa

Introduction

CS (Compressive Sensing) Radar

Numerical Results

Figure 1. Parameterε of the c2-distribution obtained from a test case with a uniform LA of size 𝑀s over 𝑀t time samples, both equal to 10, 𝑀s = 𝑀t = 10. Two point-targets are separated in u by du of 2p/𝑀s and in v by dv of 0 (top) and 2p/𝑀t (bottom).

Figure 2. Stochastic resolution bounds obtained from the same test cases as in Figure 1. The probability 𝑃res,GLRig (green crosses) obtained via IG-based GLR test

with ln aGLR IG~χε,22 is compared with the SSP

resolution 𝑃res,SSP (blue cricles).

multi-dimensional parameter space

probability of resolution assessed via a GLR test based on information distances, and compared with SSP resolution

This stochastic resolution analysis suits radar (as well as other sensors).

The performance guarantees are given by all the crucial impacts: spatial-temporal array design as well as input SNR, separation and a probability of resolution.

further interpretation of stochastic resolution bounds

all radar parameters: range, Doppler and angles

sparse sensing in the front end, and

links to the information theory

[1] A. J. den Dekker and A. van den Bos, “Resolution: a survey", J. of the Opt. Soc. of America A, 14/3, 1997.

[2] C. R. Rao. Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math.Soc. 37, pp. 81-89, 1945.

[3] S. Amari. "Information geometry of statistical inference - an overview", IEEE IT Workshop, 2002.

[4] Y. Cheng, X. Wang, T. Caelli, X. Li and B. Moran, “On information resolution of radar systems", IEEE Trans on AES 48/4, 2012.

[5] D. Donoho, “Compressed sensing,” IEEE Trans. on IT 52/4, 2005.

[6] E. de Jong and R. Pribić, “Sparse signal processing on estimation grid with constant information distance applied in radar”, EURASIP Journal on Advances in SP, 2014:78.

[7] P.P. Vaidynathan and P. Pal, “Sparse Sensing With Co-Prime Samplers and Arrays”, IEEE Trans. SP 59/2, 2011.

[8] yall1: your algorithms for L1, http://yall1.blogs.rice.edu/.

[9] R. Pribić and I. Kyriakides, “Design of Sparse-signal processing in Radar Systems,” IEEE ICASSP 2014.

[10] H. L. Van Trees. Optimum Array Processing. Wiley, 2002.

[11] R. Pribić, M. Coutino and G. Leus, “Stochastic Resolution Analysis of Co-prime Arrays in Radar”, IEEE SSP 2016.

[12] S.M Kay. Fundamentals of Statistical Signal Processing Vol. II: Detection Theory. Prentice Hall, 1998.

[13] S. T. Smith, “Statistical resolution limits and the complexified CR bounds”, IEEE Trans. on SP 53/5, 2005.

[14] Zhi Liu and A. Nehorai, “Statistical angular resolution limit for point sources”, IEEE Trans. on SP 55/11, 2007.

Stochastic Resolution Analysis via a GLR Test in Radar Radmila Pribić

Sensors Advanced Developments, Thales Nederland, Delft, The Netherlands

Resolution is primarily given by the minimum distance between two objects that still can be resolved (e.g.[1]). For the performance guarantees, a complete description needs also the probability of resolution at a given separation and signal-to-noise ratio (SNR).

For the stochastic completeness, exploring information geometry (IG, [2]-[4]) and compressive sensing (CS, [5]) suits radar ([6]).

This stochastic resolution analysis is aimed for CS radar because of critical SNR in its acquisition and high resolution from its processing.

Contributions and Conclusions

Future work

References

IEEE CoSeRa 2016, Aachen: Poster Session A7-III Sparse Reconstruction Aspects, Wednesday, 21 September, 2016

Stochastic Resolution Analysis